1. Consider the following competitive market:
Inverse of demand function: P^D(Q)=A^D-B^DQ
Production cost of each firm: TCfirm(q)=(1/2)Mq^2 + F
Free entry but exist cost of %u03C6
Assume profits per firm are %u2013%u03C6
a)Define an equilibrium for this environment
b) Solve for the equilibrium defined in (A)
c) The government wants to sell X units in this market. The cost it paid for those units is C and they were bought in a foreign market (local producers did not sell these units to the govt) Define an equilibrium for this environment.
d) Solve for the equilibrium defined in part c
e)Perform a cost benefit analysis of the project defined in part c
f) Assume that the govt wants to impose a subsidy of s percent per unit traded. Define an equilibrium for this environment
g)Assume the govt wants to buy X units in this market to give to the poor. Define an equilibrium for this environment
2.Consider the following competitive market:
Inverse of demand function: P^D(Q)=A^D-B^DQ
Production technology of each firm: AK^%u03B1L^1-%u03B1
The number of firms is N
The capital per firm is fixed and equal across firms.
The cost to enter or exit the market is very large (you can say it%u2019s infinite)
a)Define an equilibrium for this model
b)solve for equilibrium defined in part a
c)The govt wants to sell X units in this market. The cost it paid for those units is C and they were bought in a foreign market(local producers did not sell these units to the government.). Evaluate the impacts of this project. Assume that the producers were making the minimum amount of profits possible in equilibrium.
d)Show that the predictions of this model are equivalent to the predictions induced by a model in which firms have the following total cost function: TC(q)=(1/2)Mq^2 + F
e)Assume that the government wants to open this market to international trade and the international price for this good is P^int, which is higher than the price at which goods are traded when this market is closed to international trade.
3. Consider the following competitive market:
Inverse of demand function: P^D(Q)=A^D-B^DQ>WTP(Q)=A^D + E %u2013 B^DQ
Production technology of each firm: q(K,L)=min{%u03B1K,(1-%u03B1)L}
Capital per fim is fixed and equal across firms.
There is free entry and exit
a)Define a competitive equilibrium for this market
b)Compute the equilibrium you defined in part a
c)Is the quantity traded higher, lower or equal to the quantity that would maximize wealth in this market? Explain your answer.
d) To maximize total wealth in this market, the government is deciding between imposing a ta xor a subsidy. What would you recommend the government do? Explain
e)Will imposing a maximum production quota per firm increase social wealth? Explain.
